cfamounts

Cash flow and time mapping for bond portfolio

In R2017b, the specification of optional input arguments has changed. While the previous ordered inputs syntax is still supported, it may no longer be supported in a future release. Use the optional name-value pair inputs: `Period`, `Basis`, `EndMonthRule`, `IssueDate`,`FirstCouponDate`, `LastCouponDate`, `StartDate`,`Face`, `AdjustCashFlowsBasis`, `BusinessDayConvention`, `CompoundingFrequency`, `DiscountBasis`, `Holidays`, and `PrincipalType`.

Syntax

``[CFlowAmounts,CFlowDates,TFactors,CFlowFlags,CFPrincipal] = cfamounts(CouponRate,Settle,Maturity)``
``[CFlowAmounts,CFlowDates,TFactors,CFlowFlags,CFPrincipal] = cfamounts(___,Name,Value)``

Description

example

````[CFlowAmounts,CFlowDates,TFactors,CFlowFlags,CFPrincipal] = cfamounts(CouponRate,Settle,Maturity)` returns matrices of cash flow amounts, cash flow dates, time factors, and cash flow flags for a portfolio of `NUMBONDS` fixed-income securities.The elements contained in the `cfamounts` outputs for the cash flow matrix, time factor matrix, and cash flow flag matrix correspond to the cash flow dates for each security. The first element of each row in the cash flow matrix is the accrued interest payable on each bond. This accrued interest is zero in the case of all zero coupon bonds. `cfamounts` determines all cash flows and time mappings for a bond whether or not the coupon structure contains odd first or last periods. All output matrices are padded with `NaN`s as necessary to ensure that all rows have the same number of elements.```

example

````[CFlowAmounts,CFlowDates,TFactors,CFlowFlags,CFPrincipal] = cfamounts(___,Name,Value)` adds optional name-value arguments. ```

Examples

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This example shows how to compute the cash flow structure and time factors for a bond portfolio that contains a corporate bond paying interest quarterly and a Treasury bond paying interest semiannually.

```Settle = '01-Nov-1993'; Maturity = ['15-Dec-1994';'15-Jun-1995']; CouponRate= [0.06; 0.05]; Period = [4; 2]; Basis = [1; 0]; [CFlowAmounts, CFlowDates, TFactors, CFlowFlags] = ... cfamounts(CouponRate,Settle, Maturity, Period, Basis)```
```CFlowAmounts = 2×6 -0.7667 1.5000 1.5000 1.5000 1.5000 101.5000 -1.8989 2.5000 2.5000 2.5000 102.5000 NaN ```
```CFlowDates = 2×6 728234 728278 728368 728460 728552 728643 728234 728278 728460 728643 728825 NaN ```
```TFactors = 2×6 0 0.2404 0.7403 1.2404 1.7403 2.2404 0 0.2404 1.2404 2.2404 3.2404 NaN ```
```CFlowFlags = 2×6 0 3 3 3 3 4 0 3 3 3 4 NaN ```

This example shows how to compute the cash flow structure and time factors for a bond portfolio that contains a corporate bond paying interest quarterly and a Treasury bond paying interest semiannually and `CFlowDates` is returned as a datetime array.

```Settle = datetime('01-Nov-1993','Locale','en_US'); Maturity = ['15-Dec-1994';'15-Jun-1995']; CouponRate= [0.06; 0.05]; Period = [4; 2]; Basis = [1; 0]; [CFlowAmounts, CFlowDates, TFactors, CFlowFlags] = cfamounts(CouponRate,... Settle, Maturity, Period, Basis)```
```CFlowAmounts = 2×6 -0.7667 1.5000 1.5000 1.5000 1.5000 101.5000 -1.8989 2.5000 2.5000 2.5000 102.5000 NaN ```
```CFlowDates = 2x6 datetime Columns 1 through 5 01-Nov-1993 15-Dec-1993 15-Mar-1994 15-Jun-1994 15-Sep-1994 01-Nov-1993 15-Dec-1993 15-Jun-1994 15-Dec-1994 15-Jun-1995 Column 6 15-Dec-1994 NaT ```
```TFactors = 2×6 0 0.2404 0.7403 1.2404 1.7403 2.2404 0 0.2404 1.2404 2.2404 3.2404 NaN ```
```CFlowFlags = 2×6 0 3 3 3 3 4 0 3 3 3 4 NaN ```

This example shows how to compute the cash flow structure and time factors for a bond portfolio that contains a corporate bond paying interest quarterly and a Treasury bond paying interest semiannually. This example uses the following Name-Value pairs for `Period`, `Basis`, `BusinessDayConvention`, and `AdjustCashFlowsBasis`.

```Settle = '01-Jun-2010'; Maturity = ['15-Dec-2011';'15-Jun-2012']; CouponRate= [0.06; 0.05]; Period = [4; 2]; Basis = [1; 0]; [CFlowAmounts, CFlowDates, TFactors, CFlowFlags] = ... cfamounts(CouponRate,Settle, Maturity, 'Period',Period, ... 'Basis', Basis, 'AdjustCashFlowsBasis', true,... 'BusinessDayConvention','modifiedfollow')```
```CFlowAmounts = 2×8 -1.2667 1.5000 1.5000 1.5000 1.5000 1.5000 1.5000 101.5000 -2.3077 2.4932 2.5068 2.4932 2.5000 102.5000 NaN NaN ```
```CFlowDates = 2×8 734290 734304 734396 734487 734577 734669 734761 734852 734290 734304 734487 734669 734852 735035 NaN NaN ```
```TFactors = 2×8 0 0.0778 0.5778 1.0778 1.5778 2.0778 2.5778 3.0778 0 0.0769 1.0769 2.0769 3.0769 4.0769 NaN NaN ```
```CFlowFlags = 2×8 0 3 3 3 3 3 3 4 0 3 3 3 3 4 NaN NaN ```

This example shows how to use `cfamounts` with a `CouponRate` schedule. For `CouponRate` and `Face` that change over the life of the bond, schedules for `CouponRate` and `Face` can be specified with an `NINST`-by-1 cell array, where each element is a `NumDates`-by-2 matrix where the first column is dates and the second column is associated rates.

```CouponSchedule = {[datenum('15-Mar-2012') .04;datenum('15- Mar -2013') .05;... datenum('15- Mar -2015') .06]}```
```CouponSchedule = 1x1 cell array {3x2 double} ```
`cfamounts(CouponSchedule,'01-Mar-2011','15-Mar-2015' )`
```ans = 1×10 -1.8453 2.0000 2.0000 2.0000 2.5000 2.5000 3.0000 3.0000 3.0000 103.0000 ```

This example shows how to use `cfamounts` with a `Face` schedule. For `CouponRate` and `Face` that change over the life of the bond, schedules for `CouponRate` and `Face` can be specified with an `NINST`-by-1 cell array, where each element is a `NumDates`-by-2 matrix where the first column is dates and the second column is associated rates.

```FaceSchedule = {[datenum('15-Mar-2012') 100;datenum('15- Mar -2013') 90;... datenum('15- Mar -2015') 80]}```
```FaceSchedule = 1x1 cell array {3x2 double} ```
`cfamounts(.05,'01-Mar-2011','15-Mar-2015', 'Face', FaceSchedule)`
```ans = 1×10 -2.3066 2.5000 2.5000 12.5000 2.2500 12.2500 2.0000 2.0000 2.0000 82.0000 ```

This example shows how to use `cfamounts` to generate the cash flows for a sinking bond.

```[CFlowAmounts,CFDates,TFactors,CFFlags,CFPrincipal] = cfamounts(.05,'04-Nov-2010',... {'15-Jul-2014';'15-Jul-2015'},'Face',{[datenum('15-Jul-2013') 100;datenum('15-Jul-2014')... 90;datenum('15-Jul-2015') 80]})```
```CFlowAmounts = 2×11 -1.5217 2.5000 2.5000 2.5000 2.5000 2.5000 12.5000 2.2500 92.2500 NaN NaN -1.5217 2.5000 2.5000 2.5000 2.5000 2.5000 12.5000 2.2500 12.2500 2.0000 82.0000 ```
```CFDates = 2×11 734446 734518 734699 734883 735065 735249 735430 735614 735795 NaN NaN 734446 734518 734699 734883 735065 735249 735430 735614 735795 735979 736160 ```
```TFactors = 2×11 0 0.3913 1.3913 2.3913 3.3913 4.3913 5.3913 6.3913 7.3913 NaN NaN 0 0.3913 1.3913 2.3913 3.3913 4.3913 5.3913 6.3913 7.3913 8.3913 9.3913 ```
```CFFlags = 2×11 0 3 3 3 3 3 13 3 4 NaN NaN 0 3 3 3 3 3 13 3 13 3 4 ```
```CFPrincipal = 2×11 0 0 0 0 0 0 10 0 90 NaN NaN 0 0 0 0 0 0 10 0 10 0 80 ```

Input Arguments

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Annual percentage rate used to determine the coupons payable on a bond, specified as decimal using a scalar or a `NBONDS`-by-`1` vector.

`CouponRate` is `0` for zero coupon bonds.

Note

`CouponRate` and `Face` can change over the life of the bond. Schedules for `CouponRate` and `Face` can be specified with an `NBONDS`-by-`1` cell array, where each element is a `NumDates`-by-`2` matrix or cell array, where the first column is dates (serial date numbers or character vectors) and the second column is associated rates. The date indicates the last day that the coupon rate or face value is valid. This means that the corresponding `CouponRate` and `Face` value applies "on or before" the specified ending date.

Data Types: `double` | `cell` | `char`

Settlement date of the bond, specified as a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays. The `Settle` date must be before the `Maturity` date.

Data Types: `double` | `char` | `datetime`

Maturity date of the bond, specified as a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: `double` | `char` | `datetime`

Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: ```[CFlowAmounts, CFlowDates, TFactors, CFlowFlags] = ... cfamounts(CouponRate,Settle, Maturity,'Period',4,'Basis',3,'AdjustCashFlowsBasis',true,'BusinessDayConvention','modifiedfollow')```

Number of coupon payments per year for the bond, specified as the comma-separated pair consisting of `'Period'` and a scalar or a `NBONDS`-by-`1` vector using the values: `0`, `1`, `2`, `3`, `4`, `6`, or `12`.

Data Types: `double`

Day-count basis of the bond, specified as the comma-separated pair consisting of `'Basis'` and a scalar or a `NBONDS`-by-`1` vector using a supported value:

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Data Types: `double`

End-of-month rule flag, specified as the comma-separated pair consisting of `'EndMonthRule'` and a scalar or a `NBONDS`-by-`1` vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days.

• `0` = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

• `1` = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: `logical`

Bond issue date (the date the bond begins to accrue interest), specified as the comma-separated pair consisting of `'IssueDate'` and a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays. The `IssueDate` cannot be after the `Settle` date.

If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.

Data Types: `double` | `char` | `datetime`

Irregular or normal first coupon date, specified as the comma-separated pair consisting of `'FirstCouponDate'` and a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.

Note

When `FirstCouponDate` and `LastCouponDate`

are both specified, the `FirstCouponDate` takes precedence in determining the coupon payment structure. If `FirstCouponDate` is not specified, then `LastCouponDate` determines the coupon structure of the bond.

Data Types: `double` | `char` | `datetime`

Irregular or normal last coupon date, specified as the comma-separated pair consisting of `'LastCouponDate'` and a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

Note

When `FirstCouponDate` and `LastCouponDate` are both specified, the `FirstCouponDate` takes precedence in determining the coupon payment structure. If `FirstCouponDate` is not specified, then `LastCouponDate` determines the coupon structure of the bond.

Data Types: `double` | `char` | `datetime`

Forward starting date of coupon payments after the `Settle` date, specified as the comma-separated pair consisting of `'StartDate'` and a scalar or a `NBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

Note

To make an instrument forward starting, specify `StartDate` as a future date.

If you do not specify a `StartDate`, the effective start date is the `Settle` date.

Data Types: `double` | `char` | `datetime`

Face value of the bond, specified as the comma-separated pair consisting of `'Face'` and a scalar or a `NBONDS`-by-`1` vector.

Note

`CouponRate` and `Face` can change over the life of the bond. Schedules for `CouponRate` and `Face` can be specified with an `NBONDS`-by-`1` cell array where each element is a `NumDates`-by-`2` matrix or cell array, where the first column is dates (serial date numbers or character vectors) and the second column is associated rates. The date indicates the last day that the coupon rate or face value is valid. This means that the corresponding `CouponRate` and `Face` value applies "on or before" the specified ending date.

When the corresponding `Face` value is used to compute the coupon cashflow on the specified ending date. Three things happen on the specified ending date:

1. The last coupon corresponding to the current `Face` value is paid.

2. The principal differential (between the current and the next `Face` value) is paid.

3. The date marks the beginning of the period with the next `Face` value, for which the cashflow does not occur until later.

Data Types: `double` | `cell` | `char`

Adjusts cash flows according to the accrual amount based on the actual period day count, specified as the comma-separated pair consisting of `'AdjustCashFlowsBasis'` and a scalar or a `NBONDS`-by-`1` vector.

Data Types: `logical`

Business day conventions, specified as the comma-separated pair consisting of `'BusinessDayConvention'` and a scalar or `NBONDS`-by-`1` cell array of character vectors of business day conventions to be used in computing payment dates. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

• `'actual'` — Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.

• `'follow'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.

• `'modifiedfollow'` — Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.

• `'previous'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.

• `'modifiedprevious'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types: `char` | `cell`

Compounding frequency for yield calculation, specified as the comma-separated pair consisting of `'CompoundingFrequency'` and a scalar or a `NBONDS`-by-`1` vector. Values are:

• `1` — Annual compounding

• `2` — Semiannual compounding

• `3` — Compounding three times per year

• `4` — Quarterly compounding

• `6` — Bimonthly compounding

• `12` — Monthly compounding

Note

By default, SIA bases (`0`-`7`) and `BUS/252` use a semiannual compounding convention and ICMA bases (`8`-`12`) use an annual compounding convention.

Data Types: `double`

Basis used to compute the discount factors for computing the yield, specified as the comma-separated pair consisting of `'DiscountBasis'` and a scalar or a `NBONDS`-by-`1` vector. Values are:

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Note

If a SIA day-count basis is defined in the `Basis` input argument and there is no value assigned for `DiscountBasis`, the default behavior is for SIA bases to use the `actual/actual` day count to compute discount factors.

If an ICMA day-count basis or `BUS/252` is defined in the `Basis` input argument and there is no value assigned for `DiscountBasis`, the specified bases from the `Basis` input argument are used.

Data Types: `double`

Dates for holidays, specified as the comma-separated pair consisting of `'Holidays'` and a `NHOLIDAYS`-by-`1` vector of MATLAB® dates using serial date numbers, date character vectors, or datetime arrays. Holidays are used in computing business days.

Data Types: `double` | `char` | `datetime`

Type of principal when a `Face` schedule, specified as the comma-separated pair consisting of `'PrincipalType'` and a value of `'sinking'` or `'bullet'` using a scalar or a `NBONDS`-by-`1` vector.

If `'sinking'`, principal cash flows are returned throughout the life of the bond.

If `'bullet'`, principal cash flow is only returned at maturity.

Data Types: `char` | `cell`

Output Arguments

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Cash flow amounts, returned as a `NBONDS`-by-`NCFS` (number of cash flows) matrix. The first entry in each row vector is the accrued interest due at settlement. This amount could be zero, positive or negative. If no accrued interest is due, the first column is zero. If the bond is trading ex-coupon then the accrued interest is negative.

Cash flow dates for a portfolio of bonds, returned as a `NBONDS`-by-`NCFS` matrix. Each row represents a single bond in the portfolio. Each element in a column represents a cash flow date of that bond.

If all the above inputs (`Settle`, `Maturity`, `IssueDate`, `FirstCouponDate`, `LastCouponDate`, and `StartDate`) are either serial date numbers or date character vectors, then `CFlowDates` is returned as a serial date number. If any of these inputs are datetime arrays, then `CFlowDates` is returned as a datetime array.

Matrix of time factors for a portfolio of bonds, returned as a `NBONDS`-by-`NCFS` matrix. Each row corresponds to the vector of time factors for each bond. Each element in a column corresponds to the specific time factor associated with each cash flow of a bond.

Time factors are for price/yield conversion and time factors are in units of whole semiannual coupon periods plus any fractional period using an actual day count. For more information on time factors, see Time Factors.

Cash flow flags for a portfolio of bonds, returned as a `NBONDS`-by-`NCFS` matrix. Each row corresponds to the vector of cash flow flags for each bond. Each element in a column corresponds to the specific flag associated with each cash flow of a bond. Flags identify the type of each cash flow (for example, nominal coupon cash flow, front, or end partial, or "stub" coupon, maturity cash flow).

Flag

Cash Flow Type

`0`

Accrued interest due on a bond at settlement.

`1`

Initial cash flow amount smaller than normal due to a “stub” coupon period. A stub period is created when the time from issue date to first coupon date is shorter than normal.

`2`

Larger than normal initial cash flow amount because the first coupon period is longer than normal.

`3`

Nominal coupon cash flow amount.

`4`

Normal maturity cash flow amount (face value plus the nominal coupon amount).

`5`

End “stub” coupon amount (last coupon period is abnormally short and actual maturity cash flow is smaller than normal).

`6`

Larger than normal maturity cash flow because the last coupon period longer than normal.

`7`

Maturity cash flow on a coupon bond when the bond has less than one coupon period to maturity.

`8`

Smaller than normal maturity cash flow when the bond has less than one coupon period to maturity.

`9`

Larger than normal maturity cash flow when the bond has less than one coupon period to maturity.

`10`

Maturity cash flow on a zero coupon bond.

`11`

Sinking principal and initial cash flow amount smaller than normal due to a "stub" coupon period. A stub period is created when the time from issue date to first coupon date is shorter than normal.

`12`

Sinking principal and larger than normal initial cash flow amount because the first coupon period is longer than normal.

`13`

Sinking principal and nominal coupon cash flow amount.

Principal cash flows, returned as a `NBONDS`-by-`NCFS` matrix.

If `PrincipalType` is `'sinking'`, `CFPrincipal` output indicates when the principal is returned.

If `PrincipalType` is `'bullet'`, `CFPrincipal` is all zeros and, at `Maturity`, the appropriate `Face` value.

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Time Factors

Time factors help determine the present value of a stream of cash flows.

The term time factors refer to the exponent TF in the discounting equation

`$PV=\sum _{i=1}^{n}\left(\frac{CF}{{\left(1+\frac{z}{f}\right)}^{TF}}\right),$`

where:

 PV = Present value of a cash flow. CF = Cash flow amount. z = Risk-adjusted annualized rate or yield corresponding to a given cash flow. The yield is quoted on a semiannual basis. f = Frequency of quotes for the yield. Default is `2` for `Basis` values `0` to `7` and `13` and `1` for `Basis` values `8` to `12`. The default can be overridden by specifying the `CompoundingFrequency` name-value pair. TF = Time factor for a given cash flow. The time factor is computed using the compounding frequency and the discount basis. If these values are not specified, then the defaults are as follows: `CompoundingFrequency` default is `2` for `Basis` values `0` to `7` and `13` and `1` for `Basis` values `8` to `12`. `DiscountBasis` is `0` for `Basis` values `0` to `7` and `13` and the value of the input `Basis` for `Basis` values `8` to `12`.

Note

The `Basis` is always used to compute accrued interest.

References

[1] Krgin, D. Handbook of Global Fixed Income Calculations. Wiley, 2002.

[2] Mayle, J. "Standard Securities Calculations Methods: Fixed Income Securities Formulas for Analytic Measures." SIA, Vol 2, Jan 1994.

[3] Stigum, M., Robinson, F. Money Market and Bond Calculation. McGraw-Hill, 1996.